[32] Applying bifurcation theory to enzyme kinetics

Bifurcation theory is the mathematician's description of how a system changes as environmental parameters are changed. A bifurcation is a qualitative change such as a constant system suddenly oscillating as the temperature is gradually increased. This chapter discusses the Bifurcation theory and its application in enzyme kinetics. Bifurcation theory is a more systematic and general theory of nonlinear systems than the standard steady-state analysis of enzyme networks. Bifurcation theory distinguishes between local bifurcations that are analyzable in a neighborhood about a single point in state space and global bifurcations that are not. A global bifurcation usually requires additional information to what is computable by the local methods. The only global bifurcation which is discussed in this chapter is a homoclinic point. The main experimental feature of a homoclinic bifurcation is that—as a parameter is varied in a region where a stable limit cycle exists, the period will increase to infinity either exponentially or as the square root of the parameter.